Problem: $\dfrac{ -8j - 7k }{ -7 } = \dfrac{ -3j - 3l }{ -8 }$ Solve for $j$.
Multiply both sides by the left denominator. $\dfrac{ -8j - 7k }{ -{7} } = \dfrac{ -3j - 3l }{ -8 }$ $-{7} \cdot \dfrac{ -8j - 7k }{ -{7} } = -{7} \cdot \dfrac{ -3j - 3l }{ -8 }$ $-8j - 7k = -{7} \cdot \dfrac { -3j - 3l }{ -8 }$ Multiply both sides by the right denominator. $-8j - 7k = -7 \cdot \dfrac{ -3j - 3l }{ -{8} }$ $-{8} \cdot \left( -8j - 7k \right) = -{8} \cdot -7 \cdot \dfrac{ -3j - 3l }{ -{8} }$ $-{8} \cdot \left( -8j - 7k \right) = -7 \cdot \left( -3j - 3l \right)$ Distribute both sides $-{8} \cdot \left( -8j - 7k \right) = -{7} \cdot \left( -3j - 3l \right)$ ${64}j + {56}k = {21}j + {21}l$ Combine $j$ terms on the left. ${64j} + 56k = {21j} + 21l$ ${43j} + 56k = 21l$ Move the $k$ term to the right. $43j + {56k} = 21l$ $43j = 21l - {56k}$ Isolate $j$ by dividing both sides by its coefficient. ${43}j = 21l - 56k$ $j = \dfrac{ 21l - 56k }{ {43} }$